Numerical Evidence of Sinai Diffusion of Random-Mass Dirac Particles (Communications in Computational Physics, 2020)
We present quantum Lattice Boltzmann simulations of the Dirac equationfor quantum-relativistic particles with random mass. By choosing zero-average randommass fluctuation, the simulations show evidence of localization and ultra-slowSinai diffusion, due to the interference of oppositely propagating branches of the quantumwavefunction which result from random sign changes of the mass around a zero-mean.The present results indicate that the quantum lattice Boltzmann scheme mayoffer a viable tool for the numerical simulation of quantum-relativistic transport phenomenain topological materials.
Keywords: Sinai diffusion; Anderson localization; QLB method; Dirac equation; random mass.